Nuprl Lemma : page55_witness
∀[U:Type]. ∀[P,Q:U ⟶ ℙ]. ((∀x:U. (P[x] ⇒ Q[x])) ⇒ (∀x:U. P[x]) ⇒ (∀x:U. Q[x]))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
page55
Lemmas referenced :
page55
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[U:Type]. \mforall{}[P,Q:U {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:U. (P[x] {}\mRightarrow{} Q[x])) {}\mRightarrow{} (\mforall{}x:U. P[x]) {}\mRightarrow{} (\mforall{}x:U. Q[x]))
Date html generated:
2018_05_21-PM-09_03_49
Last ObjectModification:
2018_05_19-PM-05_08_17
Theory : general
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