Nuprl Lemma : assert-equal-test
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[a1,a2:A]. (f a1) = (f a2) ∈ B supposing a1 = a2 ∈ A
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
hypothesisEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[a1,a2:A]. (f a1) = (f a2) supposing a1 = a2
Date html generated:
2016_05_15-PM-03_21_24
Last ObjectModification:
2015_12_27-PM-01_04_09
Theory : general
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