Nuprl Lemma : fix-strict
∀[F:Base]. strict1(fix(F)) supposing strict2(λx,y. (F y x))
Proof
Definitions occuring in Statement :
strict2: strict2(F),
strict1: strict1(F),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strict1: strict1(F),
and: P ∧ Q,
strict2: strict2(F),
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
squash: ↓T,
has-value: (a)↓,
is-exception: is-exception(t),
nat: ℕ,
false: False,
ge: i ≥ j ,
guard: {T},
subtype_rel: A ⊆r B,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
nat_plus: ℕ+
Lemmas referenced :
fun_exp_unroll_1,
le-add-cancel,
add-zero,
add_functionality_wrt_le,
add-commutes,
add-swap,
add-associates,
minus-minus,
minus-add,
minus-one-mul-top,
zero-add,
minus-one-mul,
condition-implies-le,
less-iff-le,
not-ge-2,
false_wf,
subtract_wf,
decidable__le,
exception-not-bottom,
strictness-apply,
fun_exp0_lemma,
int_subtype_base,
less_than_wf,
ge_wf,
less_than_irreflexivity,
less_than_transitivity1,
nat_properties,
strict2_wf,
is-exception_wf,
base_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
sqequalRule,
productElimination,
thin,
lambdaFormation,
lemma_by_obid,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
hypothesis,
because_Cache,
imageElimination,
imageMemberEquality,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
axiomSqleEquality,
sqequalAxiom,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
exceptionCompactness,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
voidElimination,
applyEquality,
voidEquality,
unionElimination,
addEquality,
intEquality,
minusEquality,
dependent_set_memberEquality
Latex:
\mforall{}[F:Base]. strict1(fix(F)) supposing strict2(\mlambda{}x,y. (F y x))
Date html generated:
2016_05_13-PM-04_07_25
Last ObjectModification:
2016_01_14-PM-07_46_11
Theory : fun_1
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