Nuprl Lemma : weak-continuity-principle-nat+-int-bool-double-ext
∀F,H:(ℕ+ ⟶ ℤ) ⟶ 𝔹. ∀f:ℕ+ ⟶ ℤ. ∀G:n:ℕ+ ⟶ {g:ℕ+ ⟶ ℤ| f = g ∈ (ℕ+n ⟶ ℤ)} . ∃n:ℕ+. (F f = F (G n) ∧ H f = H (G n))
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
nat_plus: ℕ+,
bool: 𝔹,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
weak-continuity-principle-nat+-int-bool-double,
member: t ∈ T
Lemmas referenced :
weak-continuity-principle-nat+-int-bool-double
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}F,H:(\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}) {}\mrightarrow{} \mBbbB{}. \mforall{}f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}. \mforall{}G:n:\mBbbN{}\msupplus{} {}\mrightarrow{} \{g:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}| f = g\} .
\mexists{}n:\mBbbN{}\msupplus{}. (F f = F (G n) \mwedge{} H f = H (G n))
Date html generated:
2017_09_29-PM-06_06_21
Last ObjectModification:
2017_09_12-PM-02_10_28
Theory : continuity
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