Nuprl Lemma : compare-fun_wf
∀[A,B:Type]. ∀[cmp:comparison(B)]. ∀[f:A ⟶ B]. (compare-fun(cmp;f) ∈ comparison(A))
Proof
Definitions occuring in Statement :
compare-fun: compare-fun(cmp;f),
comparison: comparison(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
compare-fun: compare-fun(cmp;f),
comparison: comparison(T),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
equal-wf-T-base,
le_wf,
all_wf,
comparison_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
cumulativity,
productElimination,
lambdaFormation,
imageElimination,
extract_by_obid,
isectElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
intEquality,
dependent_functionElimination,
minusEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
independent_functionElimination,
independent_pairFormation,
productEquality,
functionEquality,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[cmp:comparison(B)]. \mforall{}[f:A {}\mrightarrow{} B]. (compare-fun(cmp;f) \mmember{} comparison(A))
Date html generated:
2017_04_17-AM-08_27_02
Last ObjectModification:
2017_02_27-PM-04_49_45
Theory : list_1
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