Nuprl Lemma : imageset_functionality
∀B1,B2,f1,f2:coSet{i:l}. (seteq(B1;B2) ⇒ seteq(f1;f2) ⇒ seteq(imageset(B1;f1);imageset(B2;f2)))
Proof
Definitions occuring in Statement :
imageset: imageset(B;f),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
exists: ∃x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
setmem-imageset,
iff_wf,
seteq_weakening,
setmem_functionality,
orderedpair-snd_wf,
seteq_wf,
coSet_wf,
exists_wf,
setmem_wf,
imageset_wf,
co-seteq-iff
Rules used in proof :
existsLevelFunctionality,
existsFunctionality,
andLevelFunctionality,
impliesFunctionality,
addLevel,
because_Cache,
lambdaEquality,
sqequalRule,
instantiate,
cumulativity,
productEquality,
independent_pairFormation,
independent_functionElimination,
productElimination,
hypothesis,
hypothesisEquality,
isectElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}B1,B2,f1,f2:coSet\{i:l\}. (seteq(B1;B2) {}\mRightarrow{} seteq(f1;f2) {}\mRightarrow{} seteq(imageset(B1;f1);imageset(B2;f2)))
Date html generated:
2018_07_29-AM-10_05_44
Last ObjectModification:
2018_07_18-PM-03_20_17
Theory : constructive!set!theory
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