Nuprl Lemma : mk_lambdas_unroll2
∀[F:Top]. ∀[m:ℕ+]. (mk_lambdas(F;m) ~ mk_lambdas(λx.F;m - 1))
Proof
Definitions occuring in Statement :
mk_lambdas: mk_lambdas(F;m),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
top: Top,
lambda: λx.A[x],
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
mk_lambdas: mk_lambdas(F;m),
top: Top,
subtract: n - m,
nat_plus: ℕ+,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
prop: ℙ,
uiff: uiff(P;Q),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
top_wf,
set_subtype_base,
sqequal-wf-base,
primrec-wf-nat-plus,
nat_plus_wf,
int_subtype_base,
all_wf,
add-subtract-cancel,
add-swap,
subtract_wf,
less_than_wf,
le-add-cancel,
add-zero,
add-associates,
add_functionality_wrt_le,
add-commutes,
minus-one-mul-top,
zero-add,
minus-one-mul,
minus-add,
condition-implies-le,
less-iff-le,
not-lt-2,
false_wf,
decidable__lt,
mk_lambdas_unroll,
nat_plus_properties,
base_wf,
primrec0_lemma,
primrec1_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
rename,
isectElimination,
hypothesisEquality,
setElimination,
dependent_set_memberEquality,
addEquality,
natural_numberEquality,
unionElimination,
independent_pairFormation,
productElimination,
independent_functionElimination,
independent_isectElimination,
applyEquality,
lambdaEquality,
intEquality,
because_Cache,
minusEquality,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
sqequalAxiom
Latex:
\mforall{}[F:Top]. \mforall{}[m:\mBbbN{}\msupplus{}]. (mk\_lambdas(F;m) \msim{} mk\_lambdas(\mlambda{}x.F;m - 1))
Date html generated:
2016_05_15-PM-02_10_02
Last ObjectModification:
2016_01_15-PM-10_21_00
Theory : untyped!computation
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